Wheel bearing apparatus is used for driving wheels and driven wheels. It has been developed where the wheel bearing apparatus is intended to be manufactured at a low cost, have a light weight and a compact size to improve fuel consumption. A known representative example of a prior art wheel bearing apparatus for a driven wheel is shown in FIG. 4.
This wheel bearing apparatus is a so called third generation type. It includes a shaft member (wheel hub) 51, an inner ring 52, an outer ring 53 and double row balls 54, 54. The shaft member 51 is integrally formed, on its one end, with a wheel mounting flange 55 to mount a wheel (not shown). The wheel hub outer circumference includes an inner raceway surface 51a. A cylindrical portion 51b axially extends from the inner raceway surface 51a. 
The inner ring 52 is formed, on its outer circumference, with an inner raceway surface 52a. The inner ring 52 is press-fit onto the cylindrical portion 51b of the shaft member 51. The inner ring 52 is prevented from coming off the shaft member 51, axially, by a caulked portion 51c. The caulked portion 51c is formed by plastically deforming the end portion of the cylindrical portion 51b of the shaft member 51 radially outward.
The outer ring 53 is formed, on its outer circumference, with a body mounting flange 53b. The outer ring inner circumference includes double row outer raceway surfaces 53a, 53a. The double row balls 54, 54 are rollably contained between the double row outer raceway surfaces 53a, 53a and the inner raceway surfaces 51a, 52a that oppose the double row outer raceway surfaces 53a, 53a. 
A cylindrical end 56 has a thickness for forming the caulked portion 51c that is reduced toward its tip end in a condition before caulking deformation of the cylindrical end 56 radially outward. The thickness of the caulked portion 51c pressing the larger end face 52b of the inner ring 52, formed by expanding the cylindrical portion 56 radially outward, is gradually reduced toward its tip end as compared with the base end of the cylindrical end 56.
Thus, it is unnecessary to apply an excessively large force to the cylindrical end 56 to plastically deform it to form the caulked portion 51c. Accordingly, it is possible to prevent the generation of cracks in the caulked portion 51c accompanied with the caulking work as well as to prevent causing an excessive deformation of the diameter of the inner ring 52 that would give influences to factors of durability such as pre-pressure and/or rolling fatigue life. Japanese Laid-open Patent Publication No. 272903/1998
Although it is possible to suppress excessive deformation of the inner ring 52 in the prior art wheel bearing apparatus, micro cracks are sometimes formed at a tip end of the caulked portion 51c. Thus, it is believed that the strength of the caulked portion 51c would be insufficient. Applicants have noticed that such a problem could be solved by appropriately selecting factors for manufacturing the wheel bearing apparatus such as materials, dimensions etc. That is, it is necessary to assure the strength of the caulked portion 51c to prevent it from being broken by an axial load and/or moment load applied to the wheel bearing apparatus since the caulked portion 51c always applies the axial force (pressing force) to the inner ring 52. To assure the strength of the caulked portion 51c, it is necessary to suppress the draft (degree of caulking). The larger the draft the more micro cracks that are caused in the tip end of the caulked portion 51c. 